Jean-Pierre Demailly

Jean-Pierre Demailly, mathematician, member of the Académie des Sciences, and professor at the University of Grenoble Alpes since 1983, passed away on March 17, 2022.

Very involved in both research and teaching at the UGA, he was a pillar of the Fourier Institute for almost 40 years. He made essential contributions to its development and its international influence throughout an exceptional scientific career.

As a junior and senior member of the Institut Universitaire de France (IUF) and as former Director of the Institut Fourier, Jean-Pierre Demailly received many distinctions and prizes during a particularly brilliant international career.

His most important mathematical contributions concern analysis and complex geometry. He was particularly innovative in his ability to develop powerful analytical tools and to apply them to deep problems in algebraic geometry. Under the direction of Henri Skoda and with support from Pierre Lelong, his first work answered a question from Jean-Pierre Serre on Stein fibered spaces. He then turned to the study of closed positive currents, their Lelong numbers, their regularization and the use of Monge-Ampère operators. His famous holomorphic Morse inequalities were published in the Annales de l'Institut Fourier in 1985. He developed and used Hörmander's L2 techniques, Dolbeault cohomology, and particularly fine curvature calculations in order to obtain vanishing theorems for line or vector bundles on algebraic varieties. The use of analytical methods allowed him to make major advances towards the Fujita conjecture in the 90's; thirty years later, his results have been only slightly improved. He developed, with several collaborators, in a spectacular way, the study of Kähler varieties and their subvarieties using powerful and fundamentally original analytic methods (introduction of singular metrics, non-vanishing theorems, characterization of the Kähler cone and of the numerically effective and pseudo-effective cones, study of varieties whose tangent bundle or anticanonical bundle is positive, etc.). He then launched a vast program of study of complex hyperbolic varieties in the direction of the Kobayashi and Green-Griffiths-Lang conjectures (study of entire curves, spaces of jets differentials and their sections) in which his technical power and virtuosity were marvelous.

His research work has inspired mathematicians from all continents, and he collaborated with the most prestigious experts in complex analysis and analytic and complex algebraic geometry, many of whom were regular visitors to the Institut Fourier over the years. Thanks to his vision, he built bridges between major mathematical domains that were previously unsuspected.

Jean-Pierre Demailly also devoted himself to the transmission of knowledge to his numerous doctoral and post-doctoral students and more generally to young researchers. He thus contributed to the development of mathematics in Tunisia, India, and China through regular visits. The list of his interventions abroad in the framework of colloquia or thematic schools is innumerable. He was also the creator and leader of the Summer School of Mathematics of the Institut Fourier, which since its inception in 1992, has welcomed each year in Grenoble for 3 weeks, more than a hundred doctoral students or post-doctoral fellows from around the world. He also gave many regular courses at the Ecole Normale Supérieure de Lyon, training several classes of students. His book on the numerical analysis of differential equations, published by the Presses Universitaires de Grenoble in 1991, is a reference for young mathematicians.

Concerned about the quality of the education provided to current generations, he was involved in the improvement of the French educational system as president of the Groupe de Réflexion Interdisciplinaire sur les Programmes, an association under the law of 1901 which is responsible for a nationwide school experiment: "Savoir Lire Écrire Compter Calculer".

He was also among the pioneers of free circulation of knowledge. His book "Complex analytic and differential geometry", a reference still today, has not ceased to grow and evolve over many years and has always been freely available on his web page. He was one of the founders of Episciences, a platform providing the scientific guarantee of an editorial committee to articles published in open archives. Also quite involved in the free software movement, Jean-Pierre Demailly has contributed to its diffusion both locally and nationally.

His personality and his passion for mathematics have left their mark on generations of students and have given rise to numerous careers in the service of science. His written work, his lectures, his research presentations, and his public presentations were always distinguished by their clarity. Generous and available, he had about twenty doctoral students, most of whom are recognized mathematicians today.